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Malcolm Turnbull told Donald Trump that Australia would take any refugee the USA nominated - including "not very attractive" ones - if the President honoured the asylum seeker relocation deal brokered with Barack Obama, according to a sensationally leaked transcript of their infamous first phone call.

Following Turnbull's commitment comment, Trump cuts him off: "Okay, this shows me to be a dope".

In a phone call with Mexican President Enrique Peña Nieto, he insisted that the two leaders stop discussing whether Mexico would pay for Trump's proposed border wall.

"This is going to kill me", he said to Turnbull on January 27 during a conversation he described as "the worst call by far" during his nascent presidency, the Washington Post reported, citing a transcript. I think it is a terrible deal, a disgusting deal that I would have never made.

Turnbull then implores Trump: "Can you hear me out Mr. President?"

"You can not say that to the press", Trump told Pena Nieto according to the transcript of the January 27 call published by the Post on Thursday.

In a similar exchange, he told Mr Trump: "You can certainly say that it was not a deal that you would have done, but you are going to stick with it". I do not know where they find these people to make these stupid deals. I will say it just that way. It is an embarrassment to me, but at least I got you off the hook.

There's more explaining and more not listening and this gem from Trump: "What is the thing with boats?"

"I hate taking these people", Trump continued.

He added that Australia would act in good faith and allow the USA to make its own decisions based on the vetting, as had always been the conditions of the deal.

Turnbull attempted to correct Trump, saying, "I would not be so sure about that".

Turnbull tries to appeal to Trump the dealmaker again: "But can I say to you, there is nothing more important in business or politics than a deal is a deal". As far as I am concerned that is enough Malcom [sic].

"Putin was a pleasant call", Trump said, referring to his conversation with the Russian leader Vladimir Putin.

"I have had it", Trump says. "I have been making these calls all day, and this is the most unpleasant call all day".

The Washington Post's explosive report also detailed Trump's conversation with Mexican President Enrique Pena Nieto in which he begged him to stop saying his government would not pay to build a border wall "because I can not live with that".

He then went on to make clear that "Putin was a pleasant call".

"Turnbull asks if Trump wants to discuss Syria and North Korea; Trump replies "...this is insane".

Mr Trump replied: "Well, it is close".

It unclear from the transcript whether this occurs, though the call does appear to end abruptly.